LMFDB - Embedded newform 740.2.ce.a.247.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [740,2,Mod(3,740)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(740, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([18, 27, 26])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("740.3"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.ce (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\Q(\zeta_{36})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{36}]$

Embedding invariants

Embedding label			247.1
Root			$0.642788 + 0.766044i$ of defining polynomial
Character	$\chi$	$=$	740.247
Dual form			740.2.ce.a.3.1

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.123257 - 1.40883i) q^{2} +(-1.96962 - 0.347296i) q^{4} +(-1.86603 + 1.23205i) q^{5} +(-0.732051 + 2.73205i) q^{8} +(2.95442 - 0.520945i) q^{9} +(1.50575 + 2.78078i) q^{10} +(5.59549 - 3.91800i) q^{13} +(3.75877 + 1.36808i) q^{16} +(-5.24685 - 3.67389i) q^{17} +(-0.369771 - 4.22650i) q^{18} +(4.10324 - 1.77860i) q^{20} +(1.96410 - 4.59808i) q^{25} +(-4.83013 - 8.36603i) q^{26} +(-2.83786 - 4.91531i) q^{29} +(2.39069 - 5.12685i) q^{32} +(-5.82260 + 6.93910i) q^{34} -6.00000 q^{36} +(-5.73520 - 2.02670i) q^{37} +(-2.00000 - 6.00000i) q^{40} +(1.89932 - 10.7716i) q^{41} +(-4.87120 + 4.61210i) q^{45} +(4.49951 + 5.36231i) q^{49} +(-6.23583 - 3.33383i) q^{50} +(-12.3817 + 5.77367i) q^{52} +(6.78568 - 3.16421i) q^{53} +(-7.27463 + 3.39222i) q^{58} +(13.3483 + 2.35366i) q^{61} +(-6.92820 - 4.00000i) q^{64} +(-5.61415 + 14.2050i) q^{65} +(9.05836 + 9.05836i) q^{68} +(-0.739541 + 8.45299i) q^{72} +(12.0263 - 12.0263i) q^{73} +(-3.56218 + 7.83013i) q^{74} +(-8.69951 + 2.07812i) q^{80} +(8.45723 - 3.07818i) q^{81} +(-14.9412 - 4.00349i) q^{82} +(14.3172 + 0.391175i) q^{85} +(3.68792 + 1.34229i) q^{89} +(5.89726 + 7.43117i) q^{90} +(-2.62860 - 9.81006i) q^{97} +(8.10919 - 5.67812i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{5} + 12 q^{8} - 24 q^{17} - 18 q^{25} - 6 q^{26} + 30 q^{34} - 72 q^{36} - 24 q^{40} + 24 q^{41} - 42 q^{58} + 72 q^{61} + 30 q^{73} + 30 q^{74} + 84 q^{85} + 60 q^{89}+O(q^{100}) $ 12 * q - 12 * q^5 + 12 * q^8 - 24 * q^17 - 18 * q^25 - 6 * q^26 + 30 * q^34 - 72 * q^36 - 24 * q^40 + 24 * q^41 - 42 * q^58 + 72 * q^61 + 30 * q^73 + 30 * q^74 + 84 * q^85 + 60 * q^89

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.123257	−	1.40883i	0.0871557	−	0.996195i
$2$	0.123257	−	1.40883i	0.0871557	−	0.996195i
$3$		0			0		0.996195	−	0.0871557i	$-0.0277778\pi$
$3$		0			0		−0.996195	+	0.0871557i	$0.972222\pi$
$4$	−1.96962	−	0.347296i	−0.984808	−	0.173648i
$5$	−1.86603	+	1.23205i	−0.834512	+	0.550990i
$5$	−1.86603	+	1.23205i	−0.834512	+	0.550990i
$6$		0			0
$7$		0			0		−0.906308	−	0.422618i	$-0.861111\pi$
$7$		0			0		0.906308	+	0.422618i	$0.138889\pi$
$8$	−0.732051	+	2.73205i	−0.258819	+	0.965926i
$9$	2.95442	−	0.520945i	0.984808	−	0.173648i
$10$	1.50575	+	2.78078i	0.476161	+	0.879358i
$11$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$11$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$12$		0			0
$13$	5.59549	−	3.91800i	1.55191	−	1.08666i	0.592153	−	0.805826i	$-0.298278\pi$
$13$	5.59549	−	3.91800i	1.55191	−	1.08666i	0.959757	−	0.280833i	$-0.0906107\pi$
$14$		0			0
$15$		0			0
$16$	3.75877	+	1.36808i	0.939693	+	0.342020i
$17$	−5.24685	−	3.67389i	−1.27255	−	0.891048i	−0.275029	−	0.961436i	$-0.588688\pi$
$17$	−5.24685	−	3.67389i	−1.27255	−	0.891048i	−0.997520	+	0.0703875i	$0.977576\pi$
$18$	−0.369771	−	4.22650i	−0.0871557	−	0.996195i
$19$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$19$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$20$	4.10324	−	1.77860i	0.917512	−	0.397708i
$21$		0			0
$22$		0			0
$23$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$23$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$24$		0			0
$25$	1.96410	−	4.59808i	0.392820	−	0.919615i
$26$	−4.83013	−	8.36603i	−0.947266	−	1.64071i
$27$		0			0
$28$		0			0
$29$	−2.83786	−	4.91531i	−0.526977	−	0.912750i	−0.999506	−	0.0314353i	$-0.989992\pi$
$29$	−2.83786	−	4.91531i	−0.526977	−	0.912750i	0.472529	−	0.881315i	$-0.343341\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	2.39069	−	5.12685i	0.422618	−	0.906308i
$33$		0			0
$34$	−5.82260	+	6.93910i	−0.998568	+	1.19005i
$35$		0			0
$36$	−6.00000			−1.00000
$37$	−5.73520	−	2.02670i	−0.942861	−	0.333187i
$37$	−5.73520	−	2.02670i	−0.942861	−	0.333187i
$38$		0			0
$39$		0			0
$40$	−2.00000	−	6.00000i	−0.316228	−	0.948683i
$41$	1.89932	−	10.7716i	0.296624	−	1.68224i	−0.363905	−	0.931436i	$-0.618557\pi$
$41$	1.89932	−	10.7716i	0.296624	−	1.68224i	0.660529	−	0.750801i	$-0.270332\pi$
$42$		0			0
$43$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$43$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$44$		0			0
$45$	−4.87120	+	4.61210i	−0.726155	+	0.687531i
$46$		0			0
$47$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$47$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$48$		0			0
$49$	4.49951	+	5.36231i	0.642788	+	0.766044i
$50$	−6.23583	−	3.33383i	−0.881879	−	0.471475i
$51$		0			0
$52$	−12.3817	+	5.77367i	−1.71703	+	0.800664i
$53$	6.78568	−	3.16421i	0.932085	−	0.434638i	0.103581	−	0.994621i	$-0.466970\pi$
$53$	6.78568	−	3.16421i	0.932085	−	0.434638i	0.828504	+	0.559983i	$0.189192\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−7.27463	+	3.39222i	−0.955206	+	0.445420i
$59$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$59$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$60$		0			0
$61$	13.3483	+	2.35366i	1.70907	+	0.301355i	0.940848	−	0.338829i	$-0.110031\pi$
$61$	13.3483	+	2.35366i	1.70907	+	0.301355i	0.768221	+	0.640184i	$0.221142\pi$
$62$		0			0
$63$		0			0
$64$	−6.92820	−	4.00000i	−0.866025	−	0.500000i
$65$	−5.61415	+	14.2050i	−0.696349	+	1.76192i
$66$		0			0
$67$		0			0		−0.906308	−	0.422618i	$-0.861111\pi$
$67$		0			0		0.906308	+	0.422618i	$0.138889\pi$
$68$	9.05836	+	9.05836i	1.09849	+	1.09849i
$69$		0			0
$70$		0			0
$71$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$71$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$72$	−0.739541	+	8.45299i	−0.0871557	+	0.996195i
$73$	12.0263	−	12.0263i	1.40757	−	1.40757i	0.635323	−	0.772246i	$-0.280867\pi$
$73$	12.0263	−	12.0263i	1.40757	−	1.40757i	0.772246	−	0.635323i	$-0.219133\pi$
$74$	−3.56218	+	7.83013i	−0.414095	+	0.910234i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$79$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$80$	−8.69951	+	2.07812i	−0.972634	+	0.232341i
$81$	8.45723	−	3.07818i	0.939693	−	0.342020i
$82$	−14.9412	−	4.00349i	−1.64998	−	0.442112i
$83$		0			0		−0.819152	−	0.573576i	$-0.805556\pi$
$83$		0			0		0.819152	+	0.573576i	$0.194444\pi$
$84$		0			0
$85$	14.3172	+	0.391175i	1.55292	+	0.0424289i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	3.68792	+	1.34229i	0.390919	+	0.142283i	0.529999	−	0.847998i	$-0.322192\pi$
$89$	3.68792	+	1.34229i	0.390919	+	0.142283i	−0.139080	+	0.990281i	$0.544415\pi$
$90$	5.89726	+	7.43117i	0.621626	+	0.783314i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−2.62860	−	9.81006i	−0.266894	−	0.996061i	−0.961081	−	0.276267i	$-0.910903\pi$
$97$	−2.62860	−	9.81006i	−0.266894	−	0.996061i	0.694187	−	0.719794i	$-0.255764\pi$
$98$	8.10919	−	5.67812i	0.819152	−	0.573576i
$99$		0			0
$100$	−5.46542	+	8.37432i	−0.546542	+	0.837432i
$101$	−9.67443	+	16.7566i	−0.962642	+	1.66734i	−0.246820	+	0.969061i	$0.579386\pi$
$101$	−9.67443	+	16.7566i	−0.962642	+	1.66734i	−0.715822	+	0.698283i	$0.753948\pi$
$102$		0			0
$103$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$103$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$104$	6.60800	+	18.1553i	0.647968	+	1.78028i
$105$		0			0
$106$	−3.62147	−	9.94990i	−0.351748	−	0.966419i
$107$		0			0		0.819152	−	0.573576i	$-0.194444\pi$
$107$		0			0		−0.819152	+	0.573576i	$0.805556\pi$
$108$		0			0
$109$	−12.8249	+	10.7614i	−1.22840	+	1.03075i	−0.230063	+	0.973176i	$0.573893\pi$
$109$	−12.8249	+	10.7614i	−1.22840	+	1.03075i	−0.998341	+	0.0575772i	$0.981662\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−17.5968	−	1.53952i	−1.65537	−	0.144826i	−0.779184	−	0.626795i	$-0.784366\pi$
$113$	−17.5968	−	1.53952i	−1.65537	−	0.144826i	−0.876188	+	0.481969i	$0.839922\pi$
$114$		0			0
$115$		0			0
$116$	3.88242	+	10.6669i	0.360473	+	0.990392i
$117$	14.4904	−	14.4904i	1.33964	−	1.33964i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−5.50000	+	9.52628i	−0.500000	+	0.866025i
$122$	4.96117	−	18.5153i	0.449163	−	1.67630i
$123$		0			0
$124$		0			0
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$		0			0
$127$		0			0		−0.422618	−	0.906308i	$-0.638889\pi$
$127$		0			0		0.422618	+	0.906308i	$0.361111\pi$
$128$	−6.48928	+	9.26765i	−0.573576	+	0.819152i
$129$		0			0
$130$	19.3205	+	9.66025i	1.69452	+	0.847260i
$131$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$131$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	13.8782	−	11.6452i	1.19005	−	0.998568i
$137$	5.85281	−	21.8430i	0.500039	−	1.86617i	0.000294847	−	1.00000i	$-0.499906\pi$
$137$	5.85281	−	21.8430i	0.500039	−	1.86617i	0.499745	−	0.866173i	$-0.333427\pi$
$138$		0			0
$139$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$139$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	11.8177	+	2.08378i	0.984808	+	0.173648i
$145$	11.3514	+	5.67571i	0.942685	+	0.471342i
$146$	−15.4607	−	18.4253i	−1.27954	−	1.52489i
$147$		0			0
$148$	10.5923	+	5.98363i	0.870679	+	0.491851i
$149$			23.5804i			1.93178i	0.258954	+	0.965890i	$0.416622\pi$
$149$			23.5804i			1.93178i	−0.258954	+	0.965890i	$0.583378\pi$
$150$		0			0
$151$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$151$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$152$		0			0
$153$	−17.4153	−	8.12090i	−1.40795	−	0.656536i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−8.52756	+	12.1786i	−0.680574	+	0.971960i	0.319132	+	0.947710i	$0.396609\pi$
$157$	−8.52756	+	12.1786i	−0.680574	+	0.971960i	−0.999706	+	0.0242497i	$0.992280\pi$
$158$		0			0
$159$		0			0
$160$	1.85545	+	12.5123i	0.146686	+	0.989183i
$161$		0			0
$162$	−3.29423	−	12.2942i	−0.258819	−	0.965926i
$163$		0			0		−0.422618	−	0.906308i	$-0.638889\pi$
$163$		0			0		0.422618	+	0.906308i	$0.361111\pi$
$164$	−7.48186	+	20.5562i	−0.584235	+	1.60517i
$165$		0			0
$166$		0			0
$167$		0			0		0.996195	−	0.0871557i	$-0.0277778\pi$
$167$		0			0		−0.996195	+	0.0871557i	$0.972222\pi$
$168$		0			0
$169$	11.5125	−	31.6303i	0.885576	−	2.43310i
$170$	2.31579	−	20.1223i	0.177613	−	1.54331i
$171$		0			0
$172$		0			0
$173$	−0.544796	+	6.22704i	−0.0414200	+	0.473433i	0.946952	+	0.321376i	$0.104145\pi$
$173$	−0.544796	+	6.22704i	−0.0414200	+	0.473433i	−0.988372	+	0.152057i	$0.951410\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	2.34563	−	5.03021i	0.175812	−	0.377031i
$179$		0			0		1.00000			$0$
$179$		0			0		−1.00000			$\pi$
$180$	11.1962	−	7.39230i	0.834512	−	0.550990i
$181$	0.162022	−	0.918873i	0.0120430	−	0.0682993i	−0.978194	−	0.207693i	$-0.933404\pi$
$181$	0.162022	−	0.918873i	0.0120430	−	0.0682993i	0.990237	+	0.139394i	$0.0445155\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	13.1990	−	3.28419i	0.970411	−	0.241458i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$		0			0
$193$	0.594690	−	2.21941i	0.0428067	−	0.159757i	−0.941214	−	0.337811i	$-0.890314\pi$
$193$	0.594690	−	2.21941i	0.0428067	−	0.159757i	0.984021	+	0.178054i	$0.0569802\pi$
$194$	−14.1447	+	2.49410i	−1.01553	+	0.179066i
$195$		0			0
$196$	−7.00000	−	12.1244i	−0.500000	−	0.866025i
$197$	26.1221	+	2.28539i	1.86112	+	0.162827i	0.961673	−	0.274201i	$-0.0884132\pi$
$197$	26.1221	+	2.28539i	1.86112	+	0.162827i	0.899448	+	0.437028i	$0.143969\pi$
$198$		0			0
$199$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$199$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$200$	11.1244	+	8.73205i	0.786611	+	0.617449i
$201$		0			0
$202$	22.4148	+	15.6950i	1.57710	+	1.10430i
$203$		0			0
$204$		0			0
$205$	9.72695	+	22.4401i	0.679360	+	1.56728i
$206$		0			0
$207$		0			0
$208$	26.3923	−	7.07180i	1.82998	−	0.490341i
$209$		0			0
$210$		0			0
$211$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$211$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$212$	−14.4641	+	3.87564i	−0.993399	+	0.266180i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	13.5802	+	19.3946i	0.919768	+	1.31357i
$219$		0			0
$220$		0			0
$221$	−43.7530			−2.94315
$222$		0			0
$223$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$223$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$224$		0			0
$225$	3.40744	−	14.6079i	0.227163	−	0.973857i
$226$	−4.33786	+	24.6012i	−0.288550	+	1.63645i
$227$		0			0		0.422618	−	0.906308i	$-0.361111\pi$
$227$		0			0		−0.422618	+	0.906308i	$0.638889\pi$
$228$		0			0
$229$	10.3423	+	28.4152i	0.683438	+	1.87773i	0.381157	+	0.924510i	$0.375526\pi$
$229$	10.3423	+	28.4152i	0.683438	+	1.87773i	0.302281	+	0.953219i	$0.402252\pi$
$230$		0			0
$231$		0			0
$232$	15.5063	−	4.15491i	1.01804	−	0.272783i
$233$	−23.6715	−	6.34277i	−1.55077	−	0.415528i	−0.621045	−	0.783775i	$-0.713292\pi$
$233$	−23.6715	−	6.34277i	−1.55077	−	0.415528i	−0.929728	+	0.368246i	$0.879958\pi$
$234$	−18.6285	−	22.2006i	−1.21778	−	1.45130i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$239$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$240$		0			0
$241$	5.18845	−	6.18336i	0.334218	−	0.398305i	−0.572596	−	0.819838i	$-0.694063\pi$
$241$	5.18845	−	6.18336i	0.334218	−	0.398305i	0.906813	+	0.421533i	$0.138508\pi$
$242$	12.7430	+	8.92276i	0.819152	+	0.573576i
$243$		0			0
$244$	−25.4735	−	9.27160i	−1.63077	−	0.593553i
$245$	−15.0028	−	4.46258i	−0.958497	−	0.285104i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	15.7437	−	1.46184i	0.995717	−	0.0924548i
$251$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$251$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	12.2567	+	10.2846i	0.766044	+	0.642788i
$257$	−2.18462	+	24.9703i	−0.136273	+	1.55761i	0.553047	+	0.833150i	$0.313465\pi$
$257$	−2.18462	+	24.9703i	−0.136273	+	1.55761i	−0.689320	+	0.724457i	$0.742091\pi$
$258$		0			0
$259$		0			0
$260$	15.9911	−	26.0287i	0.991723	−	1.61423i
$261$	−10.9448	−	13.0435i	−0.677468	−	0.807375i
$262$		0			0
$263$		0			0		−0.573576	−	0.819152i	$-0.694444\pi$
$263$		0			0		0.573576	+	0.819152i	$0.305556\pi$
$264$		0			0
$265$	−8.76378	+	14.2648i	−0.538355	+	0.876280i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	3.74167	+	2.16025i	0.228134	+	0.131713i	0.609711	−	0.792624i	$-0.291286\pi$
$269$	3.74167	+	2.16025i	0.228134	+	0.131713i	−0.381577	+	0.924337i	$0.624619\pi$
$270$		0			0
$271$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$271$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$272$	−14.6955	−	20.9874i	−0.891048	−	1.27255i
$273$		0			0
$274$	−30.0517	−	10.9379i	−1.81549	−	0.660784i
$275$		0			0
$276$		0			0
$277$	20.2943	−	1.77553i	1.21937	−	0.106681i	0.540758	−	0.841178i	$-0.318138\pi$
$277$	20.2943	−	1.77553i	1.21937	−	0.106681i	0.678611	+	0.734498i	$0.262582\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−4.41506	+	12.1303i	−0.263380	+	0.723631i	0.735554	+	0.677466i	$0.236922\pi$
$281$	−4.41506	+	12.1303i	−0.263380	+	0.723631i	−0.998934	+	0.0461646i	$0.985300\pi$
$282$		0			0
$283$		0			0		0.819152	−	0.573576i	$-0.194444\pi$
$283$		0			0		−0.819152	+	0.573576i	$0.805556\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	4.39230	−	16.3923i	0.258819	−	0.965926i
$289$	8.21769	+	22.5779i	0.483394	+	1.32811i
$290$	9.39527	−	15.2927i	0.551709	−	0.898017i
$291$		0			0
$292$	−27.8638	+	19.5105i	−1.63061	+	1.14176i
$293$	22.6915	−	1.98525i	1.32565	−	0.115980i	0.597763	−	0.801673i	$-0.296056\pi$
$293$	22.6915	−	1.98525i	1.32565	−	0.115980i	0.727890	+	0.685693i	$0.240501\pi$
$294$		0			0
$295$		0			0
$296$	9.73550	−	14.1852i	0.565864	−	0.824498i
$297$		0			0
$298$	33.2208	+	2.90644i	1.92443	+	0.168366i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−27.8080	+	12.0537i	−1.59228	+	0.690195i
$306$	−13.5875	+	23.5343i	−0.776748	+	1.34537i
$307$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$307$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$311$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$312$		0			0
$313$	12.4137	−	17.7286i	0.701664	−	1.00208i	−0.297218	−	0.954810i	$-0.596059\pi$
$313$	12.4137	−	17.7286i	0.701664	−	1.00208i	0.998882	−	0.0472702i	$-0.0150522\pi$
$314$	16.1066	+	13.5150i	0.908945	+	0.762696i
$315$		0			0
$316$		0			0
$317$	−13.4275	−	28.7953i	−0.754161	−	1.61730i	−0.786318	−	0.617822i	$-0.788015\pi$
$317$	−13.4275	−	28.7953i	−0.754161	−	1.61730i	0.0321569	−	0.999483i	$-0.489762\pi$
$318$		0			0
$319$		0			0
$320$	17.8564	−	1.07180i	0.998203	−	0.0599153i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−17.7265	+	3.12567i	−0.984808	+	0.173648i
$325$	−7.02517	−	33.4238i	−0.389686	−	1.85402i
$326$		0			0
$327$		0			0
$328$	28.0381	+	13.0744i	1.54814	+	0.721912i
$329$		0			0
$330$		0			0
$331$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$331$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$332$		0			0
$333$	−18.0000	−	3.00000i	−0.986394	−	0.164399i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	2.95690	−	2.07044i	0.161073	−	0.112784i	−0.490261	−	0.871576i	$-0.663099\pi$
$337$	2.95690	−	2.07044i	0.161073	−	0.112784i	0.651334	+	0.758791i	$0.274210\pi$
$338$	−43.1428	−	20.1178i	−2.34666	−	1.09426i
$339$		0			0
$340$	−28.0635	−	5.74277i	−1.52196	−	0.311445i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	8.70571	+	1.53505i	0.468022	+	0.0825248i
$347$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$347$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$348$		0			0
$349$	−5.50632	+	15.1285i	−0.294747	+	0.809810i	0.700609	+	0.713545i	$0.252912\pi$
$349$	−5.50632	+	15.1285i	−0.294747	+	0.809810i	−0.995356	+	0.0962646i	$0.969310\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−18.7032	+	26.7109i	−0.995471	+	1.42168i	−0.0906521	+	0.995883i	$0.528895\pi$
$353$	−18.7032	+	26.7109i	−0.995471	+	1.42168i	−0.904819	+	0.425797i	$0.859994\pi$
$354$		0			0
$355$		0			0
$356$	−6.79761	−	3.92460i	−0.360273	−	0.208004i
$357$		0			0
$358$		0			0
$359$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$359$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$360$	−9.03451	−	16.6847i	−0.476161	−	0.879358i
$361$	3.29932	+	18.7113i	0.173648	+	0.984808i
$362$	−1.27457	−	0.341519i	−0.0669898	−	0.0179499i
$363$		0			0
$364$		0			0
$365$	−7.62436	+	37.2583i	−0.399077	+	1.95019i
$366$		0			0
$367$		0			0		−0.0871557	−	0.996195i	$-0.527778\pi$
$367$		0			0		0.0871557	+	0.996195i	$0.472222\pi$
$368$		0			0
$369$		−	32.8132i		−	1.70819i
$370$	−3.00000	−	19.0000i	−0.155963	−	0.987763i
$371$		0			0
$372$		0			0
$373$	−38.3971	+	3.35931i	−1.98812	+	0.173938i	−0.988363	+	0.152115i	$0.951392\pi$
$373$	−38.3971	+	3.35931i	−1.98812	+	0.173938i	−0.999762	+	0.0218237i	$0.993053\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−35.1374	−	16.3848i	−1.80967	−	0.843862i
$378$		0			0
$379$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$379$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.819152	−	0.573576i	$-0.194444\pi$
$383$		0			0		−0.819152	+	0.573576i	$0.805556\pi$
$384$		0			0
$385$		0			0
$386$	−3.05348	−	1.11138i	−0.155418	−	0.0565676i
$387$		0			0
$388$	1.77033	+	20.2350i	0.0898749	+	1.02727i
$389$	−28.4782	−	23.8961i	−1.44390	−	1.21158i	−0.936883	−	0.349644i	$-0.886303\pi$
$389$	−28.4782	−	23.8961i	−1.44390	−	1.21158i	−0.507020	−	0.861934i	$-0.669253\pi$
$390$		0			0
$391$		0			0
$392$	−17.9440	+	8.36741i	−0.906308	+	0.422618i
$393$		0			0
$394$	6.43945	−	36.5199i	0.324415	−	1.83985i
$395$		0			0
$396$		0			0
$397$	14.7461	−	3.95120i	0.740084	−	0.198305i	0.130969	−	0.991387i	$-0.458191\pi$
$397$	14.7461	−	3.95120i	0.740084	−	0.198305i	0.609115	+	0.793082i	$0.291525\pi$
$398$		0			0
$399$		0			0
$400$	13.6731	−	14.5961i	0.683657	−	0.729803i
$401$		−	21.7321i		−	1.08525i	−0.839976	−	0.542623i	$-0.817431\pi$
$401$		−	21.7321i		−	1.08525i	0.839976	−	0.542623i	$-0.182569\pi$
$402$		0			0
$403$		0			0
$404$	24.8744	−	29.6442i	1.23755	−	1.47485i
$405$	−11.9889	+	16.1637i	−0.595735	+	0.803181i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	20.5185	−	17.2171i	1.01458	−	0.851331i	0.0256402	−	0.999671i	$-0.491838\pi$
$409$	20.5185	−	17.2171i	1.01458	−	0.851331i	0.988936	+	0.148340i	$0.0473931\pi$
$410$	32.8132	−	10.9377i	1.62053	−	0.540177i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−6.70994	−	38.0540i	−0.328982	−	1.86575i
$417$		0			0
$418$		0			0
$419$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$419$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$420$		0			0
$421$	−32.7075	−	18.8837i	−1.59406	−	0.920334i	−0.992599	−	0.121435i	$-0.961250\pi$
$421$	−32.7075	−	18.8837i	−1.59406	−	0.920334i	−0.601466	−	0.798899i	$-0.705416\pi$
$422$		0			0
$423$		0			0
$424$	3.67733	+	20.8552i	0.178587	+	1.01282i
$425$	−27.1982	+	16.9095i	−1.31930	+	0.820234i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$431$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$432$		0			0
$433$	−19.9673	−	5.35021i	−0.959565	−	0.257115i	−0.255149	−	0.966902i	$-0.582124\pi$
$433$	−19.9673	−	5.35021i	−0.959565	−	0.257115i	−0.704416	+	0.709787i	$0.748791\pi$
$434$		0			0
$435$		0			0
$436$	28.9975	−	16.7417i	1.38873	−	0.801784i
$437$		0			0
$438$		0			0
$439$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$439$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$440$		0			0
$441$	16.0869	+	13.4985i	0.766044	+	0.642788i
$442$	−5.39286	+	61.6407i	−0.256512	+	2.93195i
$443$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$443$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$444$		0			0
$445$	−8.53553	+	2.03895i	−0.404623	+	0.0966556i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−30.1870	+	10.9872i	−1.42461	+	0.518517i	−0.935383	−	0.353637i	$-0.884945\pi$
$449$	−30.1870	+	10.9872i	−1.42461	+	0.518517i	−0.489231	+	0.872154i	$0.662722\pi$
$450$	−20.1600	−	6.60103i	−0.950352	−	0.311176i
$451$		0			0
$452$	34.1244	+	9.14359i	1.60507	+	0.430078i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	6.02227	+	8.60069i	0.281710	+	0.402323i	0.934923	−	0.354851i	$-0.115468\pi$
$457$	6.02227	+	8.60069i	0.281710	+	0.402323i	−0.653213	+	0.757174i	$0.726579\pi$
$458$	41.3070	−	11.0682i	1.93015	−	0.517182i
$459$		0			0
$460$		0			0
$461$	42.2571	−	7.45106i	1.96811	−	0.347031i	0.977263	−	0.212032i	$-0.0680081\pi$
$461$	42.2571	−	7.45106i	1.96811	−	0.347031i	0.990846	−	0.134999i	$-0.0431030\pi$
$462$		0			0
$463$		0			0		−0.0871557	−	0.996195i	$-0.527778\pi$
$463$		0			0		0.0871557	+	0.996195i	$0.472222\pi$
$464$	−3.94231	−	22.3579i	−0.183017	−	1.03794i
$465$		0			0
$466$	−11.8536	+	32.5674i	−0.549106	+	1.50866i
$467$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$467$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$468$	−33.5729	+	23.5080i	−1.55191	+	1.08666i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	18.3994	−	12.8834i	0.842450	−	0.589890i
$478$		0			0
$479$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$479$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$480$		0			0
$481$	−40.0318	+	11.1302i	−1.82530	+	0.507492i
$482$	−8.07180	−	8.07180i	−0.367660	−	0.367660i
$483$		0			0
$484$	14.1413	−	16.8530i	0.642788	−	0.766044i
$485$	16.9915	+	15.0673i	0.771546	+	0.684169i
$486$		0			0
$487$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$487$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$488$	−16.2019	+	34.7451i	−0.733426	+	1.57284i
$489$		0			0
$490$	−8.13623	+	20.5864i	−0.367557	+	0.930001i
$491$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$491$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$492$		0			0
$493$	−3.16848	+	36.2159i	−0.142701	+	1.63108i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$499$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$500$	−0.118971	−	22.3604i	−0.00532055	−	0.999986i
$501$		0			0
$502$		0			0
$503$		0			0		−0.422618	−	0.906308i	$-0.638889\pi$
$503$		0			0		0.422618	+	0.906308i	$0.361111\pi$
$504$		0			0
$505$	−2.59226	−	43.1876i	−0.115354	−	1.92182i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	39.5241	−	6.96917i	1.75188	−	0.308903i	0.796575	−	0.604540i	$-0.206643\pi$
$509$	39.5241	−	6.96917i	1.75188	−	0.308903i	0.955300	+	0.295637i	$0.0955319\pi$
$510$		0			0
$511$		0			0
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$		0			0
$514$	34.9097	+	6.15553i	1.53980	+	0.271509i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−34.6990	−	25.7369i	−1.52165	−	1.12864i
$521$	34.9630	+	29.3375i	1.53176	+	1.28530i	0.779220	+	0.626751i	$0.215616\pi$
$521$	34.9630	+	29.3375i	1.53176	+	1.28530i	0.752539	+	0.658548i	$0.228829\pi$
$522$	−19.7252	+	13.8117i	−0.863348	+	0.604523i
$523$		0			0		−0.906308	−	0.422618i	$-0.861111\pi$
$523$		0			0		0.906308	+	0.422618i	$0.138889\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	19.9186	−	11.5000i	0.866025	−	0.500000i
$530$	19.0165	+	14.1049i	0.826025	+	0.612679i
$531$		0			0
$532$		0			0
$533$	−31.5754	−	67.7138i	−1.36768	−	2.93301i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	3.50462	−	5.00512i	0.151095	−	0.215786i
$539$		0			0
$540$		0			0
$541$	28.7163	+	16.5793i	1.23461	+	0.712802i	0.967987	−	0.250999i	$-0.0807592\pi$
$541$	28.7163	+	16.5793i	1.23461	+	0.712802i	0.266622	+	0.963801i	$0.414093\pi$
$542$		0			0
$543$		0			0
$544$	−31.3791	+	18.1167i	−1.34537	+	0.776748i
$545$	10.6730	−	35.8819i	0.457183	−	1.53701i
$546$		0			0
$547$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$547$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$548$	−19.1138	+	40.9896i	−0.816500	+	1.75099i
$549$	40.6625			1.73543
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		−	28.8102i		−	1.22403i
$555$		0			0
$556$		0			0
$557$	−3.61140	+	41.2784i	−0.153020	+	1.74902i	0.400599	+	0.916253i	$0.368802\pi$
$557$	−3.61140	+	41.2784i	−0.153020	+	1.74902i	−0.553619	+	0.832770i	$0.686754\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	16.5453	+	7.71521i	0.697922	+	0.325446i
$563$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$563$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$564$		0			0
$565$	34.7329	−	18.8074i	1.46123	−	0.791234i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−9.32954	+	16.1592i	−0.391115	+	0.677430i	−0.992597	−	0.121456i	$-0.961244\pi$
$569$	−9.32954	+	16.1592i	−0.391115	+	0.677430i	0.601482	+	0.798886i	$0.294577\pi$
$570$		0			0
$571$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$571$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−22.5526	−	8.20848i	−0.939693	−	0.342020i
$577$	42.4896	−	19.8132i	1.76886	−	0.824835i	0.792140	−	0.610340i	$-0.208967\pi$
$577$	42.4896	−	19.8132i	1.76886	−	0.824835i	0.976725	−	0.214496i	$-0.0688108\pi$
$578$	32.8214	−	8.79446i	1.36519	−	0.365801i
$579$		0			0
$580$	−20.3868	−	15.1213i	−0.846515	−	0.627877i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	24.0526	+	41.6603i	0.995302	+	1.72391i
$585$	−9.18653	+	44.8923i	−0.379816	+	1.85607i
$586$		−	32.2132i		−	1.33072i
$587$		0			0		0.422618	−	0.906308i	$-0.361111\pi$
$587$		0			0		−0.422618	+	0.906308i	$0.638889\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−18.7846	−	15.4641i	−0.772043	−	0.635571i
$593$	27.9243	−	27.9243i	1.14671	−	1.14671i	0.159520	−	0.987195i	$-0.449006\pi$
$593$	27.9243	−	27.9243i	1.14671	−	1.14671i	0.987195	−	0.159520i	$-0.0509945\pi$
$594$		0			0
$595$		0			0
$596$	8.18938	−	46.4443i	0.335450	−	1.90243i
$597$		0			0
$598$		0			0
$599$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$599$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$600$		0			0
$601$	−0.262724	−	1.48998i	−0.0107167	−	0.0607775i	0.978980	−	0.203954i	$-0.0653794\pi$
$601$	−0.262724	−	1.48998i	−0.0107167	−	0.0607775i	−0.989697	+	0.143177i	$0.954268\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.47372	−	24.5526i	−0.0599153	−	0.998203i
$606$		0			0
$607$		0			0		0.906308	−	0.422618i	$-0.138889\pi$
$607$		0			0		−0.906308	+	0.422618i	$0.861111\pi$
$608$		0			0
$609$		0			0
$610$	13.5542	+	40.6625i	0.548792	+	1.64638i
$611$		0			0
$612$	31.4811	+	22.0433i	1.27255	+	0.891048i
$613$	33.5408	−	15.6404i	1.35470	−	0.631708i	0.396562	−	0.918008i	$-0.370203\pi$
$613$	33.5408	−	15.6404i	1.35470	−	0.631708i	0.958140	+	0.286300i	$0.0924254\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−28.3148	−	2.47723i	−1.13991	−	0.0997293i	−0.498474	−	0.866905i	$-0.666106\pi$
$617$	−28.3148	−	2.47723i	−1.13991	−	0.0997293i	−0.641437	+	0.767175i	$0.721662\pi$
$618$		0			0
$619$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$619$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−17.2846	−	18.0622i	−0.691384	−	0.722487i
$626$	−23.4465	−	19.6740i	−0.937112	−	0.786331i
$627$		0			0
$628$	21.0256	−	21.0256i	0.839013	−	0.839013i
$629$	22.6459	+	31.7043i	0.902951	+	1.26413i
$630$		0			0
$631$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$631$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$632$		0			0
$633$		0			0
$634$	−42.2227	+	15.3678i	−1.67688	+	0.610334i
$635$		0			0
$636$		0			0
$637$	46.1865	+	12.3756i	1.82998	+	0.490341i
$638$		0			0
$639$		0			0
$640$	0.690942	−	25.2888i	0.0273119	−	0.999627i
$641$	−19.9256	+	16.7196i	−0.787014	+	0.660383i	−0.945004	−	0.327058i	$-0.893943\pi$
$641$	−19.9256	+	16.7196i	−0.787014	+	0.660383i	0.157991	+	0.987441i	$0.449498\pi$
$642$		0			0
$643$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$643$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.996195	−	0.0871557i	$-0.0277778\pi$
$647$		0			0		−0.996195	+	0.0871557i	$0.972222\pi$
$648$	2.21862	+	25.3590i	0.0871557	+	0.996195i
$649$		0			0
$650$	−47.9545	+	5.77757i	−1.88093	+	0.226615i
$651$		0			0
$652$		0			0
$653$	−4.07020	+	2.84999i	−0.159279	+	0.111529i	−0.650499	−	0.759507i	$-0.725440\pi$
$653$	−4.07020	+	2.84999i	−0.159279	+	0.111529i	0.491220	+	0.871036i	$0.336551\pi$
$654$		0			0
$655$		0			0
$656$	21.8755	−	37.8895i	0.854094	−	1.47933i
$657$	29.2657	−	41.7957i	1.14176	−	1.63061i
$658$		0			0
$659$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$659$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$660$		0			0
$661$	10.4620	+	28.7440i	0.406924	+	1.11801i	0.958799	+	0.284087i	$0.0916904\pi$
$661$	10.4620	+	28.7440i	0.406924	+	1.11801i	−0.551875	+	0.833927i	$0.686087\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−6.44512	+	24.9892i	−0.249743	+	0.968312i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−16.1529	+	34.6399i	−0.622647	+	1.33527i	0.301585	+	0.953439i	$0.402484\pi$
$673$	−16.1529	+	34.6399i	−0.622647	+	1.33527i	−0.924232	+	0.381832i	$0.875293\pi$
$674$	−2.55245	−	4.42097i	−0.0983167	−	0.170290i
$675$		0			0
$676$	−33.6603	+	58.3013i	−1.29463	+	2.24236i
$677$	−8.14355	+	30.3922i	−0.312982	+	1.16807i	0.612871	+	0.790183i	$0.290014\pi$
$677$	−8.14355	+	30.3922i	−0.312982	+	1.16807i	−0.925853	+	0.377883i	$0.876652\pi$
$678$		0			0
$679$		0			0
$680$	−11.5496	+	38.8289i	−0.442907	+	1.48902i
$681$		0			0
$682$		0			0
$683$		0			0		0.573576	−	0.819152i	$-0.305556\pi$
$683$		0			0		−0.573576	+	0.819152i	$0.694444\pi$
$684$		0			0
$685$	15.9902	+	47.9705i	0.610953	+	1.83286i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	25.5718	−	44.2917i	0.974208	−	1.68738i
$690$		0			0
$691$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$691$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$692$	3.23567	−	12.0757i	0.123002	−	0.459048i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−49.5390	+	49.5390i	−1.87642	+	1.87642i
$698$	20.6348	+	9.62218i	0.781040	+	0.364205i
$699$		0			0
$700$		0			0
$701$	−25.7329	−	30.6673i	−0.971919	−	1.15829i	−0.987374	−	0.158407i	$-0.949364\pi$
$701$	−25.7329	−	30.6673i	−0.971919	−	1.15829i	0.0154547	−	0.999881i	$-0.495080\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	35.3259	+	29.6420i	1.32951	+	1.11559i
$707$		0			0
$708$		0			0
$709$	−30.0000			−1.12667			−0.563337	−	0.826227i	$-0.690483\pi$
$709$	−30.0000			−1.12667			−0.563337	+	0.826227i	$0.690483\pi$
$710$		0			0
$711$		0			0
$712$	−6.36696	+	9.09296i	−0.238612	+	0.340773i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$719$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$720$	−24.6194	+	10.6716i	−0.917512	+	0.397708i
$721$		0			0
$722$	26.7678	−	2.34188i	0.996195	−	0.0871557i
$723$		0			0
$724$	−0.638242	+	1.75356i	−0.0237201	+	0.0651704i
$725$	−28.1748	+	3.39451i	−1.04639	+	0.126069i
$726$		0			0
$727$		0			0		−0.573576	−	0.819152i	$-0.694444\pi$
$727$		0			0		0.573576	+	0.819152i	$0.305556\pi$
$728$		0			0
$729$	23.3827	−	13.5000i	0.866025	−	0.500000i
$730$	51.5510	+	15.3338i	1.90799	+	0.567529i
$731$		0			0
$732$		0			0
$733$	−22.4813	+	48.2113i	−0.830365	+	1.78072i	−0.245923	+	0.969289i	$0.579091\pi$
$733$	−22.4813	+	48.2113i	−0.830365	+	1.78072i	−0.584442	+	0.811435i	$0.698687\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	−46.2283	−	4.04445i	−1.70169	−	0.148878i
$739$		0			0			−	1.00000i	$-0.5\pi$
$739$		0			0				1.00000i	$0.5\pi$
$740$	−27.1376	+	1.88462i	−0.997597	+	0.0692799i
$741$		0			0
$742$		0			0
$743$		0			0		0.996195	−	0.0871557i	$-0.0277778\pi$
$743$		0			0		−0.996195	+	0.0871557i	$0.972222\pi$
$744$		0			0
$745$	−29.0522	−	44.0016i	−1.06439	−	1.61209i
$746$			54.5091i			1.99572i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$751$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$752$		0			0
$753$		0			0
$754$	−27.4144	+	47.4832i	−0.998374	+	1.72923i
$755$		0			0
$756$		0			0
$757$	43.3498	+	30.3538i	1.57557	+	1.10323i	0.944986	+	0.327111i	$0.106075\pi$
$757$	43.3498	+	30.3538i	1.57557	+	1.10323i	0.630588	+	0.776118i	$0.282814\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	51.5151	+	18.7500i	1.86742	+	0.679685i	0.972243	+	0.233975i	$0.0751733\pi$
$761$	51.5151	+	18.7500i	1.86742	+	0.679685i	0.895177	+	0.445710i	$0.147049\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	42.5028	−	6.30276i	1.53669	−	0.227877i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−25.0000	−	43.3013i	−0.901523	−	1.56148i	−0.825518	−	0.564376i	$-0.809117\pi$
$769$	−25.0000	−	43.3013i	−0.901523	−	1.56148i	−0.0760054	−	0.997107i	$-0.524217\pi$
$770$		0			0
$771$		0			0
$772$	−1.94210	+	4.16486i	−0.0698979	+	0.149896i
$773$	31.8589	+	45.4992i	1.14588	+	1.63649i	0.611448	+	0.791285i	$0.290588\pi$
$773$	31.8589	+	45.4992i	1.14588	+	1.63649i	0.534437	+	0.845208i	$0.320524\pi$
$774$		0			0
$775$		0			0
$776$	28.7259			1.03120
$777$		0			0
$778$	−37.1757	+	37.1757i	−1.33281	+	1.33281i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	9.57656	+	26.3114i	0.342020	+	0.939693i
$785$	0.907968	−	33.2320i	0.0324068	−	1.18610i
$786$		0			0
$787$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$787$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$788$	−50.6567	−	13.5734i	−1.80457	−	0.483533i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	83.9117	−	39.1287i	2.97979	−	1.38950i
$794$	−3.74902	−	21.2617i	−0.133048	−	0.754551i
$795$		0			0
$796$		0			0
$797$	−42.8629	−	30.0129i	−1.51828	−	1.06311i	−0.974636	−	0.223796i	$-0.928155\pi$
$797$	−42.8629	−	30.0129i	−1.51828	−	1.06311i	−0.543645	−	0.839315i	$-0.682956\pi$
$798$		0			0
$799$		0			0
$800$	−18.8781	−	21.0622i	−0.667441	−	0.744662i
$801$	11.5949	+	2.04450i	0.409687	+	0.0722389i
$802$	−30.6168	−	2.67862i	−1.08112	−	0.0945855i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−38.6977	−	38.6977i	−1.36138	−	1.36138i
$809$	50.2711	−	18.2972i	1.76744	−	0.643295i	0.767441	−	0.641119i	$-0.221530\pi$
$809$	50.2711	−	18.2972i	1.76744	−	0.643295i	0.999998	−	0.00217593i	$-0.000692620\pi$
$810$	21.2942	+	18.8827i	0.748203	+	0.663470i
$811$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$811$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−21.7270	−	31.0293i	−0.759665	−	1.08491i
$819$		0			0
$820$	−11.3650	−	47.5765i	−0.396883	−	1.66144i
$821$	27.5342	−	10.0216i	0.960950	−	0.349757i	0.186544	−	0.982447i	$-0.440271\pi$
$821$	27.5342	−	10.0216i	0.960950	−	0.349757i	0.774406	+	0.632689i	$0.218049\pi$
$822$		0			0
$823$		0			0		−0.819152	−	0.573576i	$-0.805556\pi$
$823$		0			0		0.819152	+	0.573576i	$0.194444\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		−0.573576	−	0.819152i	$-0.694444\pi$
$827$		0			0		0.573576	+	0.819152i	$0.305556\pi$
$828$		0			0
$829$	−18.7939	−	6.84040i	−0.652737	−	0.237577i	−0.00563977	−	0.999984i	$-0.501795\pi$
$829$	−18.7939	−	6.84040i	−0.652737	−	0.237577i	−0.647098	+	0.762407i	$0.724017\pi$
$830$		0			0
$831$		0			0
$832$	−54.4387	+	4.76277i	−1.88732	+	0.165119i
$833$	−3.90777	−	44.6660i	−0.135396	−	1.54758i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$839$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$840$		0			0
$841$	−1.60686	+	2.78316i	−0.0554089	+	0.0959710i
$842$	−30.6353	+	43.7518i	−1.05576	+	1.50779i
$843$		0			0
$844$		0			0
$845$	17.4875	+	73.2069i	0.601590	+	2.51839i
$846$		0			0
$847$		0			0
$848$	29.8347	−	2.61020i	1.02453	−	0.0896346i
$849$		0			0
$850$	20.4704	+	40.4019i	0.702127	+	1.38577i
$851$		0			0
$852$		0			0
$853$	−56.6879	−	4.95955i	−1.94096	−	0.169812i	−0.950802	−	0.309798i	$-0.899739\pi$
$853$	−56.6879	−	4.95955i	−1.94096	−	0.169812i	−0.990153	+	0.139986i	$0.955294\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−41.3492	+	41.3492i	−1.41246	+	1.41246i	−0.671031	+	0.741429i	$0.734148\pi$
$857$	−41.3492	+	41.3492i	−1.41246	+	1.41246i	−0.741429	+	0.671031i	$0.765852\pi$
$858$		0			0
$859$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$859$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.0871557	−	0.996195i	$-0.472222\pi$
$863$		0			0		−0.0871557	+	0.996195i	$0.527778\pi$
$864$		0			0
$865$	−6.65543	−	12.2910i	−0.226291	−	0.417908i
$866$	−9.99865	+	27.4711i	−0.339768	+	0.933505i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−20.0121	−	42.9162i	−0.677697	−	1.45333i
$873$	−12.8765	−	27.6137i	−0.435803	−	0.934583i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−6.06610	+	22.6390i	−0.204838	+	0.764464i	0.784661	+	0.619925i	$0.212837\pi$
$877$	−6.06610	+	22.6390i	−0.204838	+	0.764464i	−0.989499	+	0.144540i	$0.953830\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	51.4925	−	18.7417i	1.73482	−	0.631425i	0.735870	−	0.677123i	$-0.236774\pi$
$881$	51.4925	−	18.7417i	1.73482	−	0.631425i	0.998955	+	0.0456985i	$0.0145514\pi$
$882$	21.0000	−	21.0000i	0.707107	−	0.707107i
$883$		0			0		−0.906308	−	0.422618i	$-0.861111\pi$
$883$		0			0		0.906308	+	0.422618i	$0.138889\pi$
$884$	86.1766	+	15.1953i	2.89843	+	0.511072i
$885$		0			0
$886$		0			0
$887$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$887$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$888$		0			0
$889$		0			0
$890$	1.82048	+	12.2764i	0.0610226	+	0.411507i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	11.7583	+	43.8827i	0.392381	+	1.46438i
$899$		0			0
$900$	−11.7846	+	27.5885i	−0.392820	+	0.919615i
$901$	−47.2284	−	8.32765i	−1.57341	−	0.277434i
$902$		0			0
$903$		0			0
$904$	17.0878	−	46.9485i	0.568333	−	1.56148i
$905$	0.829761	+	1.91426i	0.0275822	+	0.0636321i
$906$		0			0
$907$		0			0		0.996195	−	0.0871557i	$-0.0277778\pi$
$907$		0			0		−0.996195	+	0.0871557i	$0.972222\pi$
$908$		0			0
$909$	−19.8531	+	54.5459i	−0.658486	+	1.80917i
$910$		0			0
$911$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$911$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$912$		0			0
$913$		0			0
$914$	12.8592	−	7.42427i	0.425345	−	0.245573i
$915$		0			0
$916$	−10.5018	−	59.5589i	−0.346990	−	1.96788i
$917$		0			0
$918$		0			0
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$		0			0
$922$	−5.28882	−	60.4515i	−0.174178	−	1.99086i
$923$		0			0
$924$		0			0
$925$	−20.5834	+	22.3902i	−0.676779	+	0.736187i
$926$		0			0
$927$		0			0
$928$	−31.9845	+	2.79828i	−1.04994	+	0.0918581i
$929$	9.38181	+	1.65427i	0.307807	+	0.0542747i	0.325418	−	0.945570i	$-0.394495\pi$
$929$	9.38181	+	1.65427i	0.307807	+	0.0542747i	−0.0176110	+	0.999845i	$0.505606\pi$
$930$		0			0
$931$		0			0
$932$	44.4210	+	20.7138i	1.45506	+	0.678505i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	28.9808	+	50.1962i	0.947266	+	1.64071i
$937$	60.8826	+	5.32654i	1.98895	+	0.174011i	0.999594	+	0.0284889i	$0.00906953\pi$
$937$	60.8826	+	5.32654i	1.98895	+	0.174011i	0.989355	+	0.145522i	$0.0464860\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	44.7874	+	16.3013i	1.46003	+	0.531407i	0.945373	−	0.325991i	$-0.105698\pi$
$941$	44.7874	+	16.3013i	1.46003	+	0.531407i	0.514655	+	0.857397i	$0.327920\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.906308	−	0.422618i	$-0.138889\pi$
$947$		0			0		−0.906308	+	0.422618i	$0.861111\pi$
$948$		0			0
$949$	20.1739	−	114.412i	0.654873	−	3.71397i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	32.4449	+	22.7182i	1.05099	+	0.735914i	0.965494	−	0.260424i	$-0.0838624\pi$
$953$	32.4449	+	22.7182i	1.05099	+	0.735914i	0.0854999	+	0.996338i	$0.472751\pi$
$954$	−15.8827	−	27.5096i	−0.514221	−	0.890657i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−31.0000			−1.00000
$962$	10.7463	+	57.7700i	0.346476	+	1.86258i
$963$		0			0
$964$	−12.3667	+	10.3769i	−0.398305	+	0.334218i
$965$	1.62472	+	4.87417i	0.0523017	+	0.156905i
$966$		0			0
$967$		0			0		0.422618	−	0.906308i	$-0.361111\pi$
$967$		0			0		−0.422618	+	0.906308i	$0.638889\pi$
$968$	−22.0000	−	22.0000i	−0.707107	−	0.707107i
$969$		0			0
$970$	23.3216	−	22.0811i	0.748810	−	0.708980i
$971$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$971$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	46.9530	+	27.1083i	1.50293	+	0.867717i
$977$	−21.5467	+	10.0474i	−0.689341	+	0.321445i	−0.735534	−	0.677488i	$-0.763069\pi$
$977$	−21.5467	+	10.0474i	−0.689341	+	0.321445i	0.0461933	+	0.998933i	$0.485291\pi$
$978$		0			0
$979$		0			0
$980$	28.0000	+	14.0000i	0.894427	+	0.447214i
$981$	−32.2841	+	38.4747i	−1.03075	+	1.22840i
$982$		0			0
$983$		0			0		0.906308	−	0.422618i	$-0.138889\pi$
$983$		0			0		−0.906308	+	0.422618i	$0.861111\pi$
$984$		0			0
$985$	−51.5602	+	27.9191i	−1.64284	+	0.889578i
$986$	50.6316	+	8.92771i	1.61244	+	0.284316i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$991$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	4.56050	−	52.1268i	0.144433	−	1.65087i	−0.485511	−	0.874231i	$-0.661366\pi$
$997$	4.56050	−	52.1268i	0.144433	−	1.65087i	0.629943	−	0.776641i	$-0.283078\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.ce.a.247.1	yes	12
4.3	odd	2	CM	740.2.ce.a.247.1	yes	12
5.3	odd	4		740.2.ce.b.543.1	yes	12
20.3	even	4		740.2.ce.b.543.1	yes	12
37.3	even	18		740.2.ce.b.447.1	yes	12
148.3	odd	18		740.2.ce.b.447.1	yes	12
185.3	odd	36	inner	740.2.ce.a.3.1	✓	12
740.3	even	36	inner	740.2.ce.a.3.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.ce.a.3.1	✓	12	185.3	odd	36	inner
740.2.ce.a.3.1	✓	12	740.3	even	36	inner
740.2.ce.a.247.1	yes	12	1.1	even	1	trivial
740.2.ce.a.247.1	yes	12	4.3	odd	2	CM
740.2.ce.b.447.1	yes	12	37.3	even	18
740.2.ce.b.447.1	yes	12	148.3	odd	18
740.2.ce.b.543.1	yes	12	5.3	odd	4
740.2.ce.b.543.1	yes	12	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.ce (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.123257 - 1.40883i) q^{2} +(-1.96962 - 0.347296i) q^{4} +(-1.86603 + 1.23205i) q^{5} +(-0.732051 + 2.73205i) q^{8} +(2.95442 - 0.520945i) q^{9} +(1.50575 + 2.78078i) q^{10} +(5.59549 - 3.91800i) q^{13} +(3.75877 + 1.36808i) q^{16} +(-5.24685 - 3.67389i) q^{17} +(-0.369771 - 4.22650i) q^{18} +(4.10324 - 1.77860i) q^{20} +(1.96410 - 4.59808i) q^{25} +(-4.83013 - 8.36603i) q^{26} +(-2.83786 - 4.91531i) q^{29} +(2.39069 - 5.12685i) q^{32} +(-5.82260 + 6.93910i) q^{34} -6.00000 q^{36} +(-5.73520 - 2.02670i) q^{37} +(-2.00000 - 6.00000i) q^{40} +(1.89932 - 10.7716i) q^{41} +(-4.87120 + 4.61210i) q^{45} +(4.49951 + 5.36231i) q^{49} +(-6.23583 - 3.33383i) q^{50} +(-12.3817 + 5.77367i) q^{52} +(6.78568 - 3.16421i) q^{53} +(-7.27463 + 3.39222i) q^{58} +(13.3483 + 2.35366i) q^{61} +(-6.92820 - 4.00000i) q^{64} +(-5.61415 + 14.2050i) q^{65} +(9.05836 + 9.05836i) q^{68} +(-0.739541 + 8.45299i) q^{72} +(12.0263 - 12.0263i) q^{73} +(-3.56218 + 7.83013i) q^{74} +(-8.69951 + 2.07812i) q^{80} +(8.45723 - 3.07818i) q^{81} +(-14.9412 - 4.00349i) q^{82} +(14.3172 + 0.391175i) q^{85} +(3.68792 + 1.34229i) q^{89} +(5.89726 + 7.43117i) q^{90} +(-2.62860 - 9.81006i) q^{97} +(8.10919 - 5.67812i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{5} + 12 q^{8} - 24 q^{17} - 18 q^{25} - 6 q^{26} + 30 q^{34} - 72 q^{36} - 24 q^{40} + 24 q^{41} - 42 q^{58} + 72 q^{61} + 30 q^{73} + 30 q^{74} + 84 q^{85} + 60 q^{89}+O(q^{100}) \) 12 * q - 12 * q^5 + 12 * q^8 - 24 * q^17 - 18 * q^25 - 6 * q^26 + 30 * q^34 - 72 * q^36 - 24 * q^40 + 24 * q^41 - 42 * q^58 + 72 * q^61 + 30 * q^73 + 30 * q^74 + 84 * q^85 + 60 * q^89

Introduction

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